次线性碰撞振子次调和弹性解的存在性和多解性问题(英文) 被引量：1

EXISTENCE AND MULTIPLICITY OF SUBHARMONIC BOUNCING SOLUTIONS FOR SUB-LINEAR IMPACT OSCILLATORS

下载PDF

导出

摘要本文利用相平面分析方法结合Poincare-Birkhoff扭转不动点定理得到了次线性碰撞振子的无穷多次调和弹性解的存在性. In this paper,we use the phase-plane analysis combined with Poincare-Birkhoff fixed point theorem to obtain the existence and multiplicity of subharmonic bouncing solutions for sub-linear impact oscillators.

作者王志国阮春兰钱定边

机构地区苏州大学数学科学学院

出处《南京大学学报（数学半年刊）》 CAS 2010年第1期17-30,共14页 Journal of Nanjing University(Mathematical Biquarterly)

基金 Supported by the National Natural Science Foundation of China(10871142) the Post Doctor Foundation of Suzhou University(32107601).

关键词碰撞振子次线性弹性周期解相平面分析 impact oscillators sub-linear bouncing periodic solutions phase-plane analysis

分类号 O175.12 [理学—数学]

引文网络
相关文献

参考文献1

1QIAN Dingbian & SUN Xiying School of Mathematical Sciences, Suzhou University, Suzhou 215006, China,Laboratory of Mathematics for Nonlinear Sciences, Fudan University, Shanghai 200433, China.Invariant tori for asymptotically linear impact oscillators[J].Science China Mathematics,2006,49(5):669-687. 被引量：5

二级参考文献25

1[1]Lamba,H.,Chaotic,regular and unbounded behaviour in the elastic impact oscillator,Physica D,1995,82:117-135. 被引量：1
2[2]Zharnitsky,V.,Invariant tori in Hamiltonian systems with impacts,Comm.Math.Phys.,2000,211:289-302. 被引量：1
3[3]Boyland,P.,Dual billiards,twist maps and impact oscillators,Nonlinearity,1996,9:1411-1438. 被引量：1
4[4]Corbera,M.,Llibre,J.,Periodic orbits of a collinear restricted three body problem,Celestial Mech.Dynam.Astronom.,2003,86:163-183. 被引量：1
5[5]Kunze,M.,Non-smooth dynamical systems,in Lecture Notes in Math.,Vol.1744,New York:Springer-Verlag,2000. 被引量：1
6[6]Qian,D.,Torres,P.J.,Bouncing solutions of an equation with attractive singularity,Proc.Roy.Soc.Edinburgh,2004,134A:210-213. 被引量：1
7[7]Bonheure,D.,Fabry,C.,Periodic motions in impact oscillators with perfectly elastic bouncing,Nonlinearity,2002,15:1281-1298. 被引量：1
8[8]Ortega,R.,Dynamics of a forced oscillator with obstacle,in Variational and Topological Methods in the Study of Nonlinear Phenomena (eds.Banci,V.,Cerami,G.,Degiovanni,M.et al.),Boston:Birkh(a)ser,2001,77-89. 被引量：1
9[9]Qian,D.,Large amplitude periodic bouncing in impact oscillators with damping,Proc.Amer.Math.Soc.,2005,133:1797-1804. 被引量：1
10[10]Qian,D.,Torres,P.J.,Periodic motions of linear impact oscillators via the successor map,SIAM J.Math.Anal.,2005,36:1707-1725. 被引量：1

共引文献4

1何涛,丁卫.二阶非自治系统的弹性周期解[J].江苏科技大学学报（自然科学版）,2011,25(4):401-404. 被引量：2
2Wei DING,Ding Bian QIAN,Chao WANG,Zhi Guo WANG.Existence of Periodic Solutions of Sublinear Hamiltonian Systems[J].Acta Mathematica Sinica,English Series,2016,32(5):621-632. 被引量：3
3HANG Wei-tao,WANG Chao,LI Qi,YANG Xiao.Admissible Periodic Bouncing Solutions for A Class of Semi-linear and Non-conservative Impact Oscillators[J].Chinese Quarterly Journal of Mathematics,2018,33(2):111-121.
4Xing Xiu-mei,Ma Jing,Jiao Lei.Boundedness in Asymmetric Quasi-periodic Oscillations[J].Communications in Mathematical Research,2017,33(2):121-128.

同被引文献19

1钱定边,孙西瀅.渐近线性碰撞振子的不变环面[J].中国科学（A辑）,2006,36(4):418-437. 被引量：2
2Lazer A, Mckenna P. Periodic bounding for a forced linear spring with obstacle. Differential Integral Equations, 1992,5: 165-172. 被引量：1
3Qian D. Large amplitude periodic bouncing for impact oscillators with damping. Proc Amer Math Soc, 2005, 133:1797-1804. 被引量：1
4Bonheune D, Fabry C. Periodic motions in impact oscillators with perfectly elastic bouncing. Nonlinearity, 2002, 15:1281-1298. 被引量：1
5Qian D, Torres P. Bouncing solutions of an equation with attractive singularity. Proc Roy Soc Edinburgh Sect A,2004, 134: 201-213. 被引量：1
6Herrera A, Torres P. Periodic solutions and chaotic dynamics in forced impact oscillators. SIAM J Appl Dyn Syst,2013, 12: 383-414. 被引量：1
7Hale J. Ordinary differential equation. New York: Robert E Krieger Publishing Campany Huntingto, 1980. 被引量：1
8Papini D, Zanolin F. Differential equations with indefinite weight: Boundary value problems and qualitative properties of the solutions. Rend Sem Mat Univ Pol Torino, 2002, 60: 265-295. 被引量：1
9Papini D. Boundary value problems for second order differential equations with superlinear terms: A topological approach. PhD Thesis. Trrieste: Scuola Internazionale Superiore di Studi Avanzati, 2000. 被引量：1
10Papini D, Zanoni F. A topological approach to superlinear indefinite boundary-value problem. Topol Methods Nonlinear Anal, 2000, 15: 203-233. 被引量：1

引证文献1

1王超.一类超线性Hill型对称碰撞方程的周期运动[J].中国科学：数学,2014,44(3):235-248. 被引量：1

二级引证文献1

1王梓欢,王超.一类双质子弱耦合碰撞系统的对称周期解[J].数学物理学报（A辑）,2023,43(5):1427-1439.

1丁卫,钱定边.碰撞Hamiltonian系统的无穷小周期解[J].中国科学：数学,2010,40(6):563-574. 被引量：3
2MULTIPLICITY OF PERIODICSOLUTIONS OF DUFFING'S EQUATIONSWITH LIPSCHITZIAN CONDITIONMULTIPLICITY OF PERIODICSOLUTIONS OF DUFFING'S EQUATIONS WITH LIPSCHITZIAN CONDITION[J].Chinese Annals of Mathematics,Series B,2000,21(4):479-488.
3丁卫.渐近线性碰撞振子的无穷多弹性周期解的存在性[J].南京大学学报（数学半年刊）,2009,26(2):206-215.
4周育英.拟线性椭圆型方程的多解性结论[J].云南师范大学学报（自然科学版）,2000,20(5):1-4.
5尹群,洪友诚.一类二阶Hamilton系统的受迫振动[J].数学年刊（A辑）,1994,1(6):701-705. 被引量：6
6何涛,丁卫.二阶非自治系统的弹性周期解[J].江苏科技大学学报（自然科学版）,2011,25(4):401-404. 被引量：2
7古丽沙旦木.玉奴斯,阿不都卡的.吾甫,孟吉翔.B_3型量子群的Gelfand-Kirillov维数[J].新疆大学学报（自然科学版）,2016,33(4):399-406. 被引量：1
8郑承民.关于Poincare-Birkhoff扭转定理的探讨[J].石河子大学学报（自然科学版）,2006,24(3):372-373.
9阿依古力.热西提,阿布都卡的.吾甫.B_3-型量子群的Gelfand-Kirillov维数[J].四川大学学报（自然科学版）,2017,54(2):253-260.
10缪玥,阿布都卡的.吾甫.D_4型量子包络代数的Gelfand-Kirillov维数（英文）[J].数学杂志,2015,35(6):1329-1340.

南京大学学报（数学半年刊）

2010年第1期

浏览历史

内容加载中请稍等...